The qui stands alone

It is not common or grammatical in writing to use elision with qui. The example you gave is an interesting glimpse into the etymology of the locale and place name.

In speaking, the vowel [i] in qui is quite strong, and it is a subject pronoun in the usage of "qui appelle ?" Neither vowel is likely to revert completely to schwa or disappear from pronunciation like how you correctly noted that que becomes qu’+vowel. Both can be relative pronouns.

Your research cited that "Qu’appelle" is a corruption, and it is simply an historical example of l’élision. Many grammars including Lawless French enforce that there is no elision after qui. (my highlight of cf.)

after qui Je ne sais pas qui il cherche.
cf. (qu’il = que + il)

It is pronounced a longer (almost two) [i] in that example.

From CNRTL, we see no elision.

b) [Attribut] Qui es-tu? demanda-t-il (Balzac, Annette, t. 4, 1824, p.
149). c) [Régime dir.] Qui aimes-tu le mieux, homme énigmatique, dis?
ton père, ta mère, ta sœur ou ton frère? (Baudel., Poèmes prose, 1867,
p. 11).Qui as-tu choisi? (Giraudoux, Sodome, 1943, i, 4, p. 84).

There is a difference in "qu’as-tu choisi ?" and "qui as-tu choisi ?" The former asks what; the latter asks whom.

You can also see how the elision with a yod [j] could shift back from something like /kiapɛl/ to /kapɛl/ to /kəˈpɛl/ depending on the speaker and the era.

It seems obfuscated in the place name. Proper nouns rarely follow rules. Brittanica.com gives

Its French name, meaning “who calls,” was derived from its Cree Indian name Kah-tep-was (“River That Calls”), referring to the cries of a legendary spirit supposedly haunting its waters.

All in all, qui does not elide like que.